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Toward understanding of Quark-Gluon Plasma in relativistic heavy ion collisions

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Toward understanding of Quark-Gluon Plasma in relativistic heavy ion collisions

Tetsufumi Hirano

Dept. of Physics

The University of Tokyo

Introduction

Basic Checks

Energy density

Chemical and kinetic equilibrium

Dynamics of Heavy Ion Collisions

Elliptic flow

Jet quenching

Summary and Outlook

Discussion

- Matter governed by QCD, not QED
- Frontier of high energy density/temperature
Toward an ultimate matter (Maximum energy density/temperature)

- Understanding the origin of matter which evolves with our universe
- Reproduction of QGP in H.I.C.
Reproduction of “early universe” on the Earth

Quark Gluon Plasma

Hadronization

Nucleosynthesis

QGP study

Understanding

early universe

front

view

Relativistic Heavy Ion Collider(2000-)

RHIC as a time machine!

STAR

side

view

STAR

Collision energy

Multiple production

(N~5000)

Heat

100 GeV per nucleon

Au(197×100)+Au(197×100)

Bjorken(’83)

Bjorken energy density

total energy

(observables)

t: proper time

y: rapidity

R: effective transverse radius

mT: transverse mass

Stolen from Karsch(PANIC05);

Note that recent results seem to be Tc~190MeV

Well above

ec from lattice

in central

collision at RHIC,

if assuming

t=1fm/c.

ec from lattice

PHENIX(’05)

- Just a necessary condition in the sense that temperature (or pressure) is not measured.
- How to estimate tau?
- If the system is thermalized, the actual energy density is larger due to pdV work.
- Boost invariant?
- Averaged over transverse area. Effect of thickness? How to estimate area?

Gyulassy, Matsui(’84) Ruuskanen(’84)

direct

Resonance decay

Two fitting parameters: Tch, mB

T=177MeV, mB = 29 MeV

Close to Tc from lattice

- Even e+e- or pp data can be fitted well!
See, e.g., Becattini&Heinz(’97)

- What is the meaning of fitting parameters? See, e.g., Rischke(’02),Koch(’03)
- Why so close to Tc?
- No chemical eq. in hadron phase!?
- Essentially dynamical problem!

Expansion rate Scattering rate

(Process dependent)

see, e.g., U.Heinz, nucl-th/0407067

Blast wave model (thermal+boost)

Driving force of flow

pressure gradient

Inside: high pressure

Outside: vacuum (p=0)

Sollfrank et al.(’93)

Spectrum for heavier particles

is a good place to see radial flow.

Power law in pp & dAu

Convex to Power law

in Au+Au

- “Consistent” with thermal + boost picture
- Large pressure could be built up in AA collisions

O.Barannikova, talk at QM05

- Not necessary to be thermalized completely
- Results from hadronic cascade models.

- How is radial flow generated dynamically?
- Finite radial flow even in pp collisions?
- (T,vT)~(140MeV,0.2)
- Is blast wave reliable quantitatively?

- Consistency?
- Chi square minimum located a different point for f and W

- Flow profile? Freezeout hypersurface? Sudden freezeout?

- Energy density can be well above ec.
- Thermalized?

- “Temperature” can be extracted.
- Why freezeout happens so close to Tc?

- High pressure can be built up.
- Completely equilibrated?

Importance of systematic study based on dynamical framework

Freezeout

“Re-confinement”

Expansion, cooling

Thermalization

First contact

(two bunches of gluons)

Time scale

10fm/c~10-23sec

<<10-4(early universe)

Temperature scale 100MeV~1012K

y

Thickness function:

x

Gold nucleus:

r0=0.17 fm-3

R=1.12A1/3-0.86A-1/3

d=0.54 fm

Woods-Saxon nuclear density:

# of binary collisions

# of participants

sin = 42mb @200GeV

1－（survival probability）

Npart and Ncoll as a function of

impact parameter

PHENIX: Correlation btw. BBC and ZDC signals

Elliptic Flow

Ollitrault (’92)

How does the system respond to spatial anisotropy?

No secondary interaction

Hydro behavior

y

f

x

INPUT

Spatial Anisotropy

2v2

Interaction among

produced particles

dN/df

dN/df

OUTPUT

Momentum Anisotropy

0

f

2p

0

f

2p

TH&Gyulassy(’06)

QGP

mixed

hadron

Anisotropy of energy density distribution

Anisotropy of “Momentum” distribution

Zhang et al.(’99)

ideal hydro limit

: Ideal hydro

v2

: strongly

interacting

system

b = 7.5fm

t(fm/c)

generated through secondary collisions

saturated in the early stage

sensitive to cross section (~1/m.f.p.~1/viscosity)

v2 is

See, e.g. Danielewicz&Gyulassy(’85)

Assuming relativistic particles,

Perfect fluid:

l=1/sr 0

shear viscosity 0

Smearing of flow

Shear flow

Next time step

STAR(’02)

PHENIX(’03)

“Hydro limit”

response =

(output)/(input)

pT dependence

and mass ordering

Multiplicity dependence

Hydro results: Huovinen, Kolb, Heinz,…

It is found that they reproduce v2(pT) data accidentally.

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

Recent Hydro Resultsfrom Our Group

- The first principle (QuantumChromo Dynamics)

- Inputs to phenomenology (lattice QCD)

Complexity

Non-linear interactions of gluons

Strong coupling

Dynamical many body system

Color confinement

- Phenomenology (hydrodynamics)

- Experimental data
- @ Relativistic Heavy Ion Collider
- ~150 papers from 4 collaborations
- since 2000

- Static
- EoS from Lattice QCD
- Finite T, m field theory
- Critical phenomena
- Chiral property of hadron

Once one accepts local

thermalization ansatz,

life becomes very easy.

Energy-momentum:

Conserved number:

- Dynamic Phenomena in HIC
- Expansion, Flow
- Space-time evolution of
- thermodynamic variables

Freezeout

“Re-confinement”

Expansion, cooling

Thermalization

First contact

(two bunches of gluons)

- Inputs in hydrodynamic simulations:
- Initial condition
- Equation of state
- Decoupling prescription

TH et al. (’06).

- Discovery of “Large” v2 at RHIC
- v2 data are comparable with hydro results.
- Hadronic cascade cannot reproduce data.
- Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations.

Result from a hadronic cascade (JAM)

(Courtesy of M.Isse)

TH(’02); TH and K.Tsuda(’02); TH et al. (’06).

QGP+hadron

- v2 data are comparable with hydro results again around h=0
- Not a QGP gas sQGP
- Nevertheless, large discrepancy in forward/backward rapidity
- See next slides

QGP only

h=0

h<0

h>0

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

A QGP fluid surrounded

by hadronic gas

“Reynolds number”

QGP core

Matter proper part:

(shear viscosity)

(entropy density)

big

in Hadron

small

in QGP

QGP: Liquid (hydro picture)

Hadron: Gas (particle picture)

- Boltzmann Eq. for hadrons instead of hydrodynamics
- Including viscosity through finite mean free path

QGP fluid+hadron gas

QGP+hadron fluids

QGP only

- Suggesting rapid increase of entropy density
- Deconfinement makes hydro work at RHIC!?
- Signal of QGP!?

T.Hirano et al.,Phys.Lett.B636(2006)299.

20-30%

- Centrality dependence is ok
- Large reduction from pure hydro in small multiplicity events

Mass dependence is o.k.

Note: First result was obtained

by Teaney et al.

T.Hirano et al.,Phys.Lett.B636(2006)299.

hybrid model

AMPT

Adopted from S.J.Sanders

(BRAHMS) talk @ QM2006

How Fragile/Robustthe Perfect Fluid Discovery is

Pion

20-30%

Proton

Mass ordering comes from

rescattering effect. Interplay btw. radial and elliptic flows

Not a direct sign of the perfect QGP fluid

Mass dependence is o.k. from

hydro+cascade.

pions

protons

v2(pT)

v2

<pT>

pT

v2 for protons can be negative

even in positive elliptic flow

must decrease with proper time

P.Huovinen et al.,PLB503,58(01)

TH and M.Gyulassy, NPA769,71(06)

Early decoupling from the system for phi mesons

Mass ordering is generated during hadronic evolution.

TH et al., arXiv:0710.5795[nucl-th].

- 1+1D Bjorken flow Bjorken(’83)
- Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…

(Ideal)

(Viscous)

h: shear viscosity (MeV/fm2), s : entropy density (1/fm3)

h/s is a good dimensionless measure

(in the natural unit) to see viscous effects.

Shear viscosity is small in comparison with entropy density!

TH and Gyulassy (’06)

h: shear viscosity, s : entropy density

Kovtun,Son,Starinets(’05)

- Absolute value of viscosity

- Its ratio to entropy density

!

Rapid increase of entropy density can

make hydro work at RHIC.

Deconfinement Signal?!

[Pa] = [N/m2]

(Dynamical) Viscosity h:

~1.0x10-3 [Pa s] (Water20℃)

~1.8x10-5 [Pa s] (Air 20℃)

Kinetic Viscosity n=h/r:

~1.0x10-6 [m2/s] (Water20℃)

~1.5x10-5 [m2/s] (Air20℃)

hwater > hair BUT nwater < nair

Non-relativistic Navier-Stokes eq. (a simple form)

Neglecting external force and assuming incompressibility.

- Reynolds number

Iso, Mori, Namiki (’59)

R>>1

Perfect fluid

- (1+1)D Bjorken solution

- Need to solve viscous fluid dynamics in (3+1)D
- Cool! But, tough!
- Causality problem

Molnar&Gyulassy(’00)

Molnar&Huovinen(’04)

25-30%

reduction

gluonic

fluid

s ~ 15 * spert !

Caveat 1: Where is the “dilute” approximation in Boltzmann

simulation? Is l~0.1fm o.k. for the Boltzmann description?

Caveat 2: Differential v2 is tricky. dv2/dpT~v2/<pT>.

Difference of v2 is amplified by the difference of <pT>.

Caveat 3: Hadronization/Freezeout are different.

D.Teaney(’03)

- Not a result from dynamical calculation, but a “fitting” to data.
- No QGP in the model
- t0 is not a initial time, but a freeze-out time.
- Gs/t0 is not equal to h/s, but to 3h/4sT0t0 (in 1+1D).
- Being smaller T0 from pT dist., t0 should be larger (~10fm/c).

Novel initial conditions

from Color Glass Condensate

lead to large eccentricity.

Hirano and Nara(’04), Hirano et al.(’06)

Kuhlman et al.(’06), Drescher et al.(’06)

Need viscosity and/or

softer EoS in the QGP!

- Agreement btw. hydro and data comes from one particular modeling. (Glauber + ideal QGP fluid + hadron gas)
- IMO, still controversial for discovery of perfect fluid QGP.
- Check model dependences to obtain robust conclusion (and toward comprehensive understanding of the QGP from exp. data).

http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/hic/index.html